Nonlinear oscillations of a one-dimensional dielectric elastomer generator system

Abstract

The nonlinear oscillations of a dielectric elastomer generator (DEG) consisting of an oscillator and two hyperelastic membranes are investigated in this paper. Due to the finite deformations of the membranes and the Maxwell stress induced by external electric fields, the DEG can be considered as a damped nonlinear oscillator. We then develop a theoretical model for the DEG system to describe the nonlinear oscillatory behavior, which can be used to elucidate the effects of the pre-stretch, membrane size, electric charge, and forcing amplitude on the DEG. From our theoretical analysis, it is found that the Maxwell stress plays a significant role in stabilizing the oscillations of the system. In practical applications, nonlinear elastic DE films exhibit strong oscillations possibly associated with a jumping phenomenon which may be harmful to the system. To describe the jumping phenomenon, an asymptotic solution on the primary resonance is derived based on the averaging method, and the obtained asymptotic solutions are further validated by the corresponding numerical results. The evolutions of the jumping phenomena with respect to the relevant factors are further analyzed. It is found that by tuning the membrane size, electric charge amount, or forcing amplitude, the jumping phenomenon can be avoided. Finally, the onsets of the jumping phenomenon are acquired from the graphic representation of the evolutions of the system resonance characteristics. It is anticipated that the current analysis could provide useful insights into designs of DE generators.